Answer :
To simplify the expression
[tex]$$14\, x^5\left(13\, x^2 + 13\, x^5\right),$$[/tex]
we follow these steps:
1. Multiply the constants:
The constant outside the parentheses is [tex]$14$[/tex] and each term inside the parentheses has a factor of [tex]$13$[/tex]. Multiplying these gives:
[tex]$$14 \times 13 = 182.$$[/tex]
2. Simplify the variable factors:
- For the first term:
Multiply [tex]$x^5$[/tex] by [tex]$x^2$[/tex]. Since exponents add when multiplying like bases, we have:
[tex]$$x^5 \cdot x^2 = x^{5+2} = x^7.$$[/tex]
- For the second term:
Multiply [tex]$x^5$[/tex] by [tex]$x^5$[/tex]:
[tex]$$x^5 \cdot x^5 = x^{5+5} = x^{10}.$$[/tex]
3. Write the simplified expression:
Combining the results from the above steps, the expression simplifies to:
[tex]$$182\, x^7 + 182\, x^{10}.$$[/tex]
Thus, the simplified form of the expression is:
[tex]$$\boxed{182\, x^7 + 182\, x^{10}}.$$[/tex]
[tex]$$14\, x^5\left(13\, x^2 + 13\, x^5\right),$$[/tex]
we follow these steps:
1. Multiply the constants:
The constant outside the parentheses is [tex]$14$[/tex] and each term inside the parentheses has a factor of [tex]$13$[/tex]. Multiplying these gives:
[tex]$$14 \times 13 = 182.$$[/tex]
2. Simplify the variable factors:
- For the first term:
Multiply [tex]$x^5$[/tex] by [tex]$x^2$[/tex]. Since exponents add when multiplying like bases, we have:
[tex]$$x^5 \cdot x^2 = x^{5+2} = x^7.$$[/tex]
- For the second term:
Multiply [tex]$x^5$[/tex] by [tex]$x^5$[/tex]:
[tex]$$x^5 \cdot x^5 = x^{5+5} = x^{10}.$$[/tex]
3. Write the simplified expression:
Combining the results from the above steps, the expression simplifies to:
[tex]$$182\, x^7 + 182\, x^{10}.$$[/tex]
Thus, the simplified form of the expression is:
[tex]$$\boxed{182\, x^7 + 182\, x^{10}}.$$[/tex]
